If cosec θ = 25/7 , find cot θ where θ is an acute angle.

Solution:

cosecθ = 25 [Given] 7

But,

cosecθ = r y

Comparing the above two table we can conclude that,

r = 25    and y = 7

By Pythagoras theorem,

r2 = x2 + y2

∴ 252 = x2 + 72

∴ 625 = x2 + 49

∴ 625 – 49 = x2

∴ 576 = x2

∴ x = ±√576

∴ x = ± 24

But, θ is an acute angle,

∴ All trigonometric values are positive

∴ x = 24

Now we need,

cot θ   = x = 24 y 7

Ans. cotθ = 24/7